The GMC Owners Group

A bone stock 4wd K1500 could be had with 265/75R16 tires; that is equal to 31.65" in height. There is no way you need 3" of lift to clear 1.5" worth of extra tire height. Well, actually half that because it is mounted to the hub, so you have .75" worth of extra tire to clear.

A 285/75R16 can be mounted to the stock truck... Equal height is 32.83" via unit conversion.

So you could easily run the 33" tires with a little cranking of the torsion bars. A 2" body lift would easily give you the clearance needed. The only spot you would have potential contact would be the rear part of the front fender during a full-lock turn and the front suspension gets compressed.

2" body lift will not be enough to interfere with the shifter. You may need to adjust your linkage if it is warn as you may not be able to select 4L as easily.
Transmission is shifted via cable, remove a cable mount and you're good.
No carpet removal. All body mount bolts are accessed from underneath the truck. The 'nut' is mounted to the body; you just need a ratchet.
Easiest way to do this is to use a 2-post vehicle lift, just lift the cab straight up off the frame. In your drive way do it one side at a time. Place a block of wood between a jack to help disperse the weight so you don't damage the floor pans.

It can be done in a day with a buddy and some good jacks. The vehicle lift makes it go a whole lot quicker.